A dartboard has been partitioned into 12 sectors of various sizes. A dart will be thrown at the board at random, and you will be awarded a cash prize depending on the size of the sector where it lands. The smaller the sector, the larger the prize. More precisely, the prize is 1/x dollars, where x is the fraction of the board occupied by the sector the dart lands in. For example, if the sector takes up 1/10 of the board's area, you win $10. What is the expected monetary value of this game